Pith Number

pith:ILMOCKKJ

pith:2006:ILMOCKKJO32V4CH54DEY7SLG67

not attested not anchored not stored refs pending

6j-symbols, hyperbolic structures and the Volume Conjecture

Francesco Costantino

arxiv:math/0611399 v4 · 2006-11-13 · math.GT · math.QA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ILMOCKKJO32V4CH54DEY7SLG67}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T02:37:59.499985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42d8e1294976f55e08fde0c98fc966f7d0d0b351283b4e674dc5b6648f3c6746

Aliases

arxiv: math/0611399 · arxiv_version: math/0611399v4 · doi: 10.48550/arxiv.math/0611399 · pith_short_12: ILMOCKKJO32V · pith_short_16: ILMOCKKJO32V4CH5 · pith_short_8: ILMOCKKJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ILMOCKKJO32V4CH54DEY7SLG67 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 42d8e1294976f55e08fde0c98fc966f7d0d0b351283b4e674dc5b6648f3c6746

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04b1485c3a0e4f66a8bf18b2a43055a1a75869b86b7551e019bbef876abaf84d",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2006-11-13T18:51:54Z",
    "title_canon_sha256": "17ddda290f0a407c96f99c184bef2612d3f6f12e3cf2b7d991943b306101859b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611399",
    "kind": "arxiv",
    "version": 4
  }
}